Mechanisms of marine invertebrate sperm chemotaxis: from cellular signaling to flagellar swimming

为了充分了解精子是如何到达卵子的，我们需要了解精子是如何根据周围环境改变其波形的。由于精子运动是一个复杂系统的紧急属性，我们需要多尺度模型来解释化学信号、力学和流体动力学。对于海洋无脊椎动物的精子，化学引诱剂能够通过启动导致钙增加的信号通路将精子引导到卵子。钙的增加改变了波形，最终改变了轨迹。该项目将开发一个层次模型，用于研究化学趋向性的相关生物化学，钙是如何和在哪里作用来改变鞭毛波形的，以及这是如何与允许精子到达卵子的轨迹相结合的。一个趋化信号通路的模型将被开发，几何离合器假说将被实施，以获得钙如何影响动力蛋白臂激活的准确模型（鞭毛轴突中的主动力和扭矩发生器）。将开发多尺度模型，将细胞水平上的相关生物化学与宏观尺度上的轨迹和鞭毛弯曲结合起来。为了准确地解释由Stokes方程控制的三维流体中鞭毛的非平面弯曲，我们将提出一种新的正则化的广义浸入边界法。该方法将为数值求解一个耦合系统提供一个框架，该系统包括一个浸入粘性流体中的结构，其中精子鞭毛对流体施加的力和扭矩可能取决于生物化学。通过综合多尺度模型的发展，我们将研究在海洋环境中，鞭毛内的趋化性和由此产生的钙浓度的增加如何使无脊椎动物精子到达并使卵子受精。即将开发的模型框架将允许我们测试关于钙在鞭毛中的作用的不同假设，以了解它如何与精子的涌现波形和轨迹相结合。这项研究是数学和生物学的结合，因为有必要考虑相关的生物化学、力学和流体动力学来模拟精子的运动。参与该研究项目的学生将接受跨学科培训，并将获得基于该项目相关生物学和计算方面的模型开发经验。虽然该项目的主要重点是研究无脊椎动物精子运动的各个方面，但即将开发的新的数值方法也将适用于研究其他微生物（如大肠杆菌）的运动方面。该项目的目的是建立数学模型，以了解海胆精子如何在海洋环境中到达卵子并使其受精。这项研究还将揭示哺乳动物精子运动的各个方面，并将与诊断不孕症和开发避孕药有关。

In order to fully understand how the sperm reaches the egg, we need to have an understanding of how the sperm is able to modify its waveform in response to the surrounding environment. Since sperm motility is an emergent property of a complex system, we need to have multiscale models that account for chemical signaling, mechanics, and hydrodynamics. For marine invertebrate sperm, a chemoattractant is able to guide sperm to the egg by initiating a signaling pathway that results in an increase in calcium. This increase in calcium modifies the waveform, and ultimately the trajectory. This project will develop a hierarchy of models that will be used to investigate the relevant biochemistry of chemotaxis, how and where calcium is acting to modify the flagellar waveform, and how this couples to trajectories that allow the sperm to reach the egg. A model for the chemotactic signaling pathway will be developed and the Geometric Clutch Hypothesis will be implemented to have an accurate model of how calcium effects dynein arm activation (active force and torque generators in the axoneme of the flagellum). Multiscale models will be developed to couple the relevant biochemistry at the cellular level to trajectories and flagellar bending at the macroscale. In order to accurately account for nonplanar bending of the flagellum in a 3-dimensional fluid governed by the Stokes equations, we will develop a new regularized formulation of the generalized immersed boundary method. This method will provide a framework to numerically solve a coupled system that includes an immersed structure in a viscous fluid, where the force and torque that the sperm flagellum exerts on the fluid can depend on the biochemistry. Through the development of integrative, multiscale models, we will examine how chemotaxis and the resulting increase in calcium concentration within the flagellum enables invertebrate sperm to reach and fertilize the egg in a marine environment. The modeling framework that will be developed will allow us to test different hypotheses about where calcium is acting in the flagellum to understand how this couples to emergent waveforms and trajectories of sperm. This research lies at the interface of mathematics and biology, as it is necessary to account for the relevant biochemistry, mechanics, and hydrodynamics to model sperm motility. Students involved in this research project will receive interdisciplinary training and will gain experience in model development based on the relevant biology and computational aspects of the project. Although the main focus of this project is on studying aspects of invertebrate sperm motility, the new numerical method that will be developed will also be applicable to study aspects of motility in other microorganisms such as Escherichia coli. The aim of this project is to develop mathematical models to understand how sea urchin sperm reach and fertilize the egg in a marine environment. This research will also shed light onto aspects of mammalian sperm motility and will be relevant to diagnosing infertility and developing contraceptives.